Question

Find the 7th term of the geometric sequence with the given terms:
a2 = 768 and a4 = 48; a7 = _____.

Answer 1

did you even try this one by yourself? or did you just post it up?! haha

Answer 2

I tried it haha. I tried to see what the difference was between 768 and 48, then I thought I had to divide that number, but that wasn't the way. @robz8

Answer 3

well you COULD divide that 768 by 48 to see the difference

Answer 4

768/48 = 16

Answer 5

Oh

Answer 6

The geometric sequence if you expand it divides each term by 2

Answer 7

since it is a geometric series, we know that we have to multiply common number to get the next number in the series

Answer 8

@galacticwavesXX actually it is each term by 4

Answer 9

ohh yea my bad its 4 i calculated it wrong in my head

Answer 10

So now that we know each term is multiplied by 1/4 to get the next number, we can take 48 and multiply it by 1/4 three times to get a7

Answer 11

\[\Large a _{n} = a _{1} r ^{n-1 }\]

So we know a2 and a4, which means

\[\Large a _{2} = a _{1} r ^{2-1 } = 768\]
\[\Large a _{4} = a _{1} r ^{4-1 } = 48\]
or
\[\Large a _{1} r = 768\]
\[\Large a _{1} r ^{3 } = 48\]

Answer 12

so what is \[48 * (1/4)^3\] @Emilyh117

Answer 13

I got 3 @robz8

Answer 14

@robz8 why did you multiply 48 by (1/3)^3 that part confuses me?

Answer 15

close... you only did it twice! you need to do it 3 times! @Emilyh117

Answer 16

i mean 1/4*

Answer 17

@galacticwavesXX the numbers are dividing by 4 each time... which is the same as multiplying by (1/4)

Answer 18

Oh. 3/4 @robz8

Answer 19

there ya go! @Emilyh117

Answer 20

ohh ok didn't know you could do it that way

Answer 21

Math is so annoying sometimes haha. Thank you. :) @robz8

Answer 22

Note that you can find a1 and r from these two, and use it to find any term of the sequence...
\[\Large a _{1} r = 768\]
\[\Large a _{1} r ^{3 } = 48 \]

Answer 23

@Emilyh117 The good part about math is that it never lies to you!

Answer 24

No, but it confuses you and stuff.. @robz8

Answer 25

@Emilyh117 only if you let it confuse you!

Answer 26

Math is my worst subject @robz8

Answer 27

but... but.... it's the coolest subject! @Emilyh117

Answer 28

Haha It's my worst. I hate it because I don't understand it very well, so it makes me mad. @robz8